Joint state-parameter estimation for tumor growth model

Annabelle Collin (1, 2) , Thibaut Kritter (2) , Clair Poignard (2) , Olivier Saut (2)

1 IMB - Institut de Mathématiques de Bordeaux
2 MONC - Modélisation Mathématique pour l'Oncologie

We present a shape-oriented data assimilation strategy suitable for front-tracking tumor growth problems. A general hyperbolic/elliptic tumor growth model is presented as well as the available observations corresponding to the location of the tumor front over time extracted from medical imaging as MRI or CT scans. We provide sufficient conditions allowing to design a state observer by proving the convergence of the observer model to the target solution, for exact parameters. In particular, the similarity measure chosen to compare observations and simulation of tumor contour is presented. A specific joint state-parameter correction with a Luenberger observer correcting the state and a reduced-order Kalman filter correcting the parameters is introduced and studied. We then illustrate and assess our proposed observer method with synthetic problems. Our numerical trials show that state estimation is very effective with the proposed Luenberger observer, but specific strategies are needed to accurately perform parameter estimation in a clinical context. We then propose strategies to deal with the fact that data is very sparse in time and that the initial distribution of the proliferation rate is unknown. The results on synthetic data are very promising and work is ongoing to apply our strategy on clinical cases.

Mots clés: Tumor growth; Data assimilation; Image processing; Front propagation

Domaines: Optimisation et contrôle [math.OC]; Equations aux dérivées partielles [math.AP]; Analyse numérique [math.NA]

Annabelle Collin, Thibaut Kritter, Clair Poignard, Olivier Saut. Joint state-parameter estimation for tumor growth model. SIAM Journal on Applied Mathematics, 2021, 81 (2), ⟨10.1137/20M131775X⟩. ⟨hal-02960283⟩